Model Error Compensator(MEC): Enhance the Robustness of Existing Control Systems with Simple Compensation

This article provides a detailed summary of the Model Error Compensator (MEC). Videos, related articles, related papers, and MATLAB links related to the Model Error Compensator are placed at the bottom.

The "Model Error Compensator" is a general-purpose method for enhancing the robustness (resilience to disturbances and model errors) of control systems. It can be used to improve the robustness of existing control systems or to enhance robustness when used in conjunction with nominal control methods. For detailed formula derivations and theory, please refer to the manuscripts and related papers at the bottom.

Author: National university faculty member in Japan with 20 years of control engineering research

This article is based on the following comprehensive papers.

>>（総合論文，計測と制御PDF）モデル誤差抑制補償器を用いた既存制御系のロバスト化 (Free access, J-Stage)

>> H. Okajima, Model Error Compensator for adding Robustness toward Existing Control Systems, IFAC PaperOnLine, Vol. 56, Issue 2, pp. 3998 - 4005 (2023) (Free access, Elsevier)

>>Researchgate (PDF) Model Error Compensator for adding Robustness toward Existing Control Systems

Overview of the Model Error Compensator
Control Simulation of MEC
Robustification of Nonlinear Systems with MEC
Robustification of Non-minimum Phase Systems with MEC
Examples of Integration with Existing Control Systems
Comparison between Disturbance Observer and Model Error Compensator
Relationship between Robust Control and Model Error Compensator
Case Study: Robustification of PID Control Systems with MEC
Research Achievements of Model Error Compensator

Overview of the Model Error Compensator

The control objective of the Model Error Compensator (MEC) is to compensate (enhance the robustness of) the input-output characteristics of the control system so that the input-output relationship becomes as close as possible to the model dynamics. This enables adding robustness against disturbances and modeling errors to existing control systems. The compensator structure is simple and can be used in combination with various control systems. Examples include nonlinear systems, non-minimum phase systems, MIMO systems, and others. It can also be combined with various control methods such as PID control and MPC (Model Predictive Control) to achieve good robust performance. From the perspective of combining with various theories widely deployed in the field of control engineering, it is compatible with quite a wide range of theories.

Note on Terminology: The Model Error Compensator (MEC) is known in Japanese as "モデル誤差抑制補償器" (Model Gosa Yokusei Hoshōki). Both terms refer to the same control methodology and are used interchangeably in academic literature.

Structure of the Model Error Compensator

As shown in the figure, MEC consists of a simple compensator structure comprising Model Pn and the Error Compensator D. For the simplest type of SISO, relative degree 1, minimum phase control object, the error compensator D can be configured with simple high-gain feedback, making it possible to bring the effective input-output characteristics (infinitely) close to those of the model. By controlling the compensated system as the control object, the entire control system can achieve the desired control. Even for more complex classes of control objects, the basic approach is high-gain feedback, and design methodologies based on trade-offs when noise is present have also been established.

The figure shows an example of control using a feedforward compensator, where compensation with MEC can be seen to suppress the effects of variations in control object dynamics.

Control Simulation of MEC

Numerical simulations are shown using MATLAB and Python.

MATLAB simulation for unstable plant

Application examples to unstable systems is shown as follow. Here, we show simulation results for an unstable system as a numerical example to confirm the effectiveness of the Model Error Compensator.

Here, we deal with the following object as the control target.

$P(s) = \frac{b+\delta b}{s -(a+\delta a)}$

In this article, we set $a = b = 1$ , and the range of $\delta a, \delta b$ is $\pm 0.1$ .

Case Without Error

First, we show the results of applying a feedback proportional controller $C = 2$ for the case without model error.

The control results (unit feedback control, step response) are as follows.

Next, we show the results when MEC is constructed by defining the error compensator as follows.

$D = 50 + \frac{50}{s}$

The error compensator has a PI control structure. It constitutes high-gain feedback. The control structure including MEC is given as follows.

The obtained response waveform is as follows.

It can be seen that the response waveforms are almost unchanged.

Case With Error

We show the respective response waveforms for cases with error. We randomly select 10 values of $\delta a, \delta b$ within the range and overlay their response waveforms. First is the case without MEC.

Case Without MEC (10 Types of Control Objects Including Variations)

Next is the response waveform for the case with MEC.

MEC + Feedback Control (10 Types of Control Objects Including Variations)

By constructing a control system that includes MEC, it can be confirmed that the effects of variations in $\delta a, \delta b$ hardly appear in the output.

MATLAB simulation for unstable 2nd order system

As the next control object, we deal with the following.

$P(s) = (c+\delta c)\frac{s+b+\delta b}{s -(a+\delta a)(s+5)}$

In this article, we set $a = 1, b = 2, c = 1.5$ , and the range of $\delta a, \delta b, \delta c$ is $\pm 0.1$ . The proportional feedback is set as $C = 5$ .

Without MEC

Checking the variations without MEC, the results are as follows.

With MEC

The response for the case with MEC is here.

Similarly, by constructing a control system that includes MEC, it can be confirmed that the effects of variations in $\delta a, \delta b$ hardly appear in the output.

Finally, we show the MATLAB code.

clear;
close all;
a = 1;
b = 1;
for i = 1:10
delb = -0.1+0.2*rand();
dela = -0.1+0.2*rand();
P=tf([b+delb],[1 -a-dela]);
Pn = tf([b],[1 -a]);
C=2;
%C=tf([2.5 0.005],[1 0]);
D=tf([50 50],[1 0]);
% MECなし
feedback(P*C,1);
figure(1)
step(ans)
xlabel('Time')
ylabel('Out')
title('Usual')
xlim([0 6])
ylim([0 3])
hold on
% MECあり
feedback(Pn*C,1)*feedback(P*D,1)-feedback(C,Pn)*feedback(P,D);
figure(2)
step(ans)
xlabel('Time')
ylabel('Out')
title('With MEC')
xlim([0 6])
ylim([0 3])
hold on
end

We confirmed the effectiveness of MEC for unstable control objects.

Python Simulation of MEC

This is a free control simulation using Python. Code can be obtained and executed on Google Colaboratory.

The control object is configured as follows.

\begin{eqnarray} P = \frac{K}{Ts+1}\frac{1}{s+2} \end{eqnarray}

Here, $T$ and $K$ include ±10% error.

Control Object (Various Objects, Variations)

On the other hand, the control object compensated by MEC shows suppressed response variations as follows.

Since MEC is applied to control systems that include controllers, the closed-loop system responses are also shown.

By applying MEC, it can be confirmed that variations in closed-loop responses are also suppressed and no steady-state error remains. If you want to reduce the error further, you can change the parameters of the error compensator.

The code is as follows. We change various transfer function coefficients to represent variations in control specifications. The first response shows the response of the system compensated with MEC and the control object, while the latter shows the closed-loop response.

Installation

!pip install control numpy matplotlib

Python Code

import numpy as np
import matplotlib.pyplot as plt
import control.matlab as control_matlab

# Based on the MATLAB code (assuming the transfer functions are defined within the script)
# Let's assume the MATLAB code has something like:
# % Mechanical system transfer function (e.g., from motor voltage to load speed)
# pm_num = [1];
# pm_den = [0.1, 1]; # Example: 0.1s + 1
# pm = tf(pm_num, pm_den);

# % Disturbance transfer function (e.g., from disturbance torque to load speed)
# d_num = [0.5];
# d_den = [0.1, 1]; # Example: 0.5 / (0.1s + 1)
# d = tf(d_num, d_den);

# % Controller transfer function (e.g., a simple proportional controller)
# c_num = [10]; # Example: Kp = 10
# c_den = [1];
# c = tf(c_num, c_den);

# Define the transfer function pm based on the MATLAB code
# pm = tf([1],[1 3 2]);
pm_num = [1]
pm_den = [1, 3, 2]
pm = control_matlab.tf(pm_num, pm_den)

# Define the transfer function d based on the MATLAB code (High Gain)
# d = tf([300 100],[1 0]);
d_num = [300, 100]
d_den = [1, 0]
d = control_matlab.tf(d_num, d_den)

# Define the transfer function c based on the MATLAB code
# c = tf([3 5],[1]);
c_num = [3, 5]
c_den = [1]
c = control_matlab.tf(c_num, c_den)

# Print the defined transfer functions
print("Transfer function pm:")
print(pm)

print("\nTransfer function d:")
print(d)

print("\nTransfer function c:")
print(c)

# k = [0.9,1.1,1,1,0.9,1.1,0.95,1.05];
# t = [1,1,0.9,1.1,0.9,1.1,1.05,0.95];
ks = [0.9, 1.1, 1, 1, 0.9, 1.1, 0.95, 1.05]
ts = [1, 1, 0.9, 1.1, 0.9, 1.1, 1.05, 0.95]

time_vector = np.linspace(0, 10, 500) # Define a suitable time vector for step response

# Create separate figures for MEC on and MEC off open-loop responses
plt.figure() # Figure for Open-loop, MEC on
plt.title('Open-Loop System Step Response (MEC On)')
plt.xlabel('Time')
plt.ylabel('Output')
plt.grid(True)

plt.figure() # Figure for Open-loop, MEC off
plt.title('Open-Loop System Step Response (MEC Off)')
plt.xlabel('Time')
plt.ylabel('Output')
plt.grid(True)

# for k in ks:
#     for t in ts:
for i in range(len(ks)): # Iterate using index to access corresponding k and t
    k = ks[i]
    t = ts[i]
    # Calculate the plant transfer function p
    # p = tf([k(i)],[t(i) 1])*tf([1],[1 2]);
    p = control_matlab.tf([k], [t, 1]) * control_matlab.tf([1], [1, 2])

    # Calculate the compensated plant pc using the MEC formula
    # pc = p*(1+pm*d)/(1+p*d);
    pc = p * (1 + pm * d) / (1 + p * d)

    # Calculate step response for pc (MEC On)
    yout_pc, T_pc = control_matlab.step(pc, time_vector)
    plt.figure(1) # Select the first figure (MEC On)
    plt.plot(T_pc, yout_pc, label=f'pc (k={k}, t={t})') # Plot on the same figure

    # Calculate step response for p (MEC Off)
    yout_p, T_p = control_matlab.step(p, time_vector)
    plt.figure(2) # Select the second figure (MEC Off)
    plt.plot(T_p, yout_p, linestyle='-', label=f'p (k={k}, t={t})') # Plot on the same figure

# Add legends and save figures after the loop
plt.figure(1)
plt.legend()
plt.savefig("open_loop_mec_on_step_responses.png")

plt.figure(2)
plt.legend()
plt.savefig("open_loop_mec_off_step_responses.png")

plt.show()
plt.close('all') # Close all figures

Additionally, effectiveness has been demonstrated on various objects including applications to benchmark problems and electric wheelchairs (where dynamics change significantly with passengers).

Robustification of Nonlinear Systems with MEC

Here, we introduce a robust feedback linearization method as an application example of the Model Error Compensator to nonlinear systems (nonlinear state equations). One powerful approach for controlling nonlinear systems is to use controllers for linear systems after linearization. Feedback linearization is a widely known method for linearizing nonlinear systems. However, feedback linearization is vulnerable to model errors because it linearizes by canceling nonlinear terms, making the absence of model errors a prerequisite for its use. It also requires all state variables of the nonlinear system.

In contrast, using MEC enables robust linearization of the entire system by considering feedback to the model. It is also characterized as an output feedback type feedback linearization method.

For robustification methods of nonlinear systems, please refer to the following papers.

モデル誤差抑制補償に基づく非線形システムのフィードバック線形化 (jst.go.jp)

モデル誤差抑制補償器に基づくロバスト経路追従制御 (jst.go.jp)

Robustification of Non-minimum Phase Systems with MEC

For non-minimum phase systems, MEC can be applied, but high-gain feedback is difficult. To provide design methods without detailed knowledge in the design of error compensator D, we have proposed a method that combines parallel feedforward compensators. The basic perspective for zero setting of parallel feedforward filters and combined design with error compensators becomes better compared to MEC alone.

Model Error Compensator with Parallel Feedforward Filter

For robustification of non-minimum phase systems, please refer to the following papers.

Full article: Model error compensator design for continuous- and discrete-time non-minimum phase systems with polytopic-type uncertainties (tandfonline.com)

Model Error Compensator with Parallel Feed-Forward Filter: SICE Journal of Control, Measurement, and System Integration: Vol 10, No 5 (tandfonline.com)

非最小位相系に対するモデル誤差抑制補償器の設計 (jst.go.jp)

Examples of Integration with Existing Control Systems

Various examples of combining existing control systems with MEC can be cited. The following figure shows examples of integration with existing methods such as PID control, model predictive control, and state feedback control.

Comparison between Disturbance Observer and Model Error Compensator

MEC and Disturbance Observer have similar stances and concepts for integration with other methods, and are often compared. The Disturbance Observer itself was proposed by Professor Kiyoshi Ohishi and Professor Kouhei Ohnishi, and has been used generically not only in the field of control engineering but from ancient times. (For example, please see Introduction to Disturbance Observer.) The differences between the MEC and Disturbance Observer are summarized below.

Disturbance Observer

Requires inverse model
Uses filters (for minimum phase systems) close to gain 1 and zero phase lag

Model Error Compensator

Does not require inverse model
Uses high-gain filters (if sensor noise is minimal)

To achieve the same disturbance rejection performance, both Disturbance Observer and MEC can be designed and often produce equivalent performance. However, when noise increases or the model structure of the object becomes complex, filter gain adjustment becomes necessary for both. In some cases, performance varies depending on this design. In MEC, design is considered with a simple loop of control object and error compensator, so the applicability of existing robust control theory and other controller design theories is high. Which one to use would be case-by-case.

MEC can handle a wide range of application classes including nonlinear systems and non-minimum phase systems/unstable control objects because it does not require an inverse model. Since research on non-minimum phase correspondence has also been conducted for Disturbance Observers, it would be rational to try both during implementation and choose the better one.

Relationship between Robust Control and Model Error Compensator

Robust control is an important control strategy that established an era in the field of control engineering. In general robust control methods, research has progressed centered on developments in the direction of optimizing worst-case performance, specifically focusing on variations and disturbances. As a problem setting, the design policy is to optimize worst-case performance within the range of control object variations. As a result, the problem of handling not only nominal but also control objects as sets becomes quite complex, and while improved robustness can be expected, the structure of evaluation functions that can be handled is limited. Moreover, it becomes difficult to balance with performance other than robust indices (such as improving nominal performance).

On the other hand, MEC can be designed to focus specifically on model error and disturbance rejection performance, while response performance and tracking control performance can be left to existing methods, resulting in high versatility. Of course, the discussion of robust control versus MEC is not correct, and the error compensator D included in MEC can also be designed based on knowledge from robust control.

Case Study: Robustification of PID Control Systems with MEC

Integration with Model Predictive Control

The compatibility with control methods like Model Predictive Control, where control input design is based on model dynamics, is also relatively high. After designing control input using model states, robustness can be ensured by MEC.

MEC MATLAB Code (Github)

MATLAB code related to MEC is available on Github. Since it corresponds to papers, please refer to it together with the papers.

Basic Control System MATLAB Code

The following two papers:

"A design method of model error compensator for systems with polytopic-type uncertainty and disturbances(2021)"

"Model Error Compensator Design for Continuous- and Discrete-Time Non-minimum Phase Systems with Polytopic-Type Uncertainties(2022)"

The corresponding MATLAB code is here.

GitHub - Hiroshi-Okajima/Robust-control-MATLAB_MEC01: model error compensator (matlab codes of journal article) robust control

Design MATLAB Code Based on Trade-offs with Sensor Noise

The following corresponds to MATLAB code for センサノイズ環境下でのモデル誤差抑制補償器の設計.

GitHub - Hiroshi-Okajima/MATLAB_MEC02_sensor_noise: disturbance-rejection by MEC

MATLAB Code for Non-minimum Phase Systems and Dead-time Systems Compensation with Parallel Feedforward Compensator

By combining with parallel feedforward compensators, robustification becomes possible for objects like non-minimum phase systems and dead-time systems where error compensation is difficult.

GitHub - Hiroshi-Okajima/MATLAB_MEC03_withPFC: control-systems

MATLAB Code for Robustification of Nonlinear Control Systems

The following is MATLAB code for robust feedback linearization for nonlinear systems.

GitHub - Hiroshi-Okajima/non_linear_control_MATLAB_MEC04: nonlinear control system, non-linear system

Signal Limitation Filter MATLAB Code

The following is MATLAB code for signal limitation filters (filters that satisfy acceleration and velocity constraints) proposed based on the MEC structure.

GitHub - Hiroshi-Okajima/MATLAB_MEC05_signal_limitation_filter: velocity acceleration limitation filter based on mec

MATLAB Code for Application of Model Error Compensator to Vehicle Control Systems

The following corresponds to MATLAB code for モデル誤差抑制補償器に基づくロバスト経路追従制御.

GitHub - Hiroshi-Okajima/Vehicle_control_MEC05

MATLAB Code for Integration with PID Control

The following is MATLAB code for robust control systems combining MEC with PID control.

GitHub - Hiroshi-Okajima/MEC05-rengo2022

The following is a video explaining MEC. It's a 30-minute video explaining the overall concept, so please watch it.

youtu.be

Related articles on the Model Error Compensator are here.

Research Topic: Model Error Compensator (control-theory.com)

Professor Kawada's article on MEC and Disturbance Observer.

『外乱相殺仕事人！！ MEC と外乱オブザーバ』

Research Achievements of Model Error Compensator

Academic Papers (with Links)

Research achievements to date are as follows.

[19] H. Okajima, Model Error Compensator for adding Robustness toward Existing Control Systems, Preprints of the IFAC World Congress, pp. 3998 - 4005 (2023) IFAC-PapersOnLine

[18] 岡島寛，モデル誤差抑制補償器を用いた既存制御系のロバスト化，計測と制御，Vol. 62，No. 3，168-175 (2023)

[17] Ryuichiro Yoshida, Hiroshi Okajima and Takumi Sato, Model error compensator design for continuous- and discrete-time non-minimum phase systems with polytopic-type uncertainties, SICE Journal of Control, Measurement, and System Integration, Volume 15 Issue 2 pags 141-153 (T&F, Open Access)

[16] R. Yoshida, Y. Tanigawa, H. Okajima and N. Matsunaga, A design method of model error compensator for systems with polytopic-type uncertainty and disturbances，SICE Journal of Control, Measurement, and System Integration Volume 14, Issue 2 (2021) (Open access)

[15] Hiroshi Okajima,Yuta Nakabayashi and Nobutomo Matsunaga, Signal-Limitation Filters to Simultaneously Satisfy Constraints of Velocity and Acceleration Signals, SICE Journal of Control, Measurement, and System Integration，Vol.13, No.1, pp.1-8 (2020) (Open access)

[14] 岡島寛：ポリトープ型不確かさを有する連続時間線形時不変システムに対するモデル誤差抑制補償器のロバスト性能解析，計測自動制御学会論文集，Vol. 55, No. 12, (2019)

[13] 岡島寛，奥村洸祐，松永信智：モデル誤差抑制補償器を用いた車輪型倒立振子のロバスト速度補償，電気学会論文誌(C), Vol. 139, No. 3, (2019)

[12] 松永信智，坂本将一，田中友樹，岡島寛：モデル誤差抑制補償器を用いたSSV型パーソナルビークルの操縦支援制御系の設計と屋外走行評価，機械学会論文誌C編，Vol. 84，No. 858, 17-00349 (2018) j-stage

[11] 岡島寛，中林佑多，松永信智：任意信号に対して速度·加速度を制約する信号制限フィルタの設計，計測自動制御学会論文集，Vol.54, No.1，pp.146-152(2018) j-stage

[10] 奥村洸佑，岡島寛，松永信智：センサノイズ環境下でのモデル誤差抑制補償器の設計，システム制御情報学会論文誌，Vol.30，No.4，pp.153-155 (2017) j-stage

[9] G. Ichimasa, H. Okajima, K. Okumura and N. Matsunaga：Model Error Compensator with Parallel Feed-Forward Filter, SICE Journal of Control, Measurement, and System Integration，Vol.10, No.5, pp.468-475 (2017) (Open access)

[8] 岡島寛，松永信智：モデル誤差抑制補償器に基づくロバスト経路追従制御，システム制御情報学会論文誌，Vol.29，No.10，pp.466-468（2016） j-stage

[7] 菅野達也，壇裕介，岡島寛，松永信智：モデル誤差抑制補償器による福祉用パーソナルビークルのロバストな屋内隊列走行システムの走行評価，機械学会論文集(Ｃ),Vol.82, No.840, pp.15-00690 (2016) j-stage

[6] 岡島寛，一政豪，松永信智：非最小位相系に対するモデル誤差抑制補償器の設計，計測自動制御学会論文集，Vol.51, No.11, pp.794-801 (2015) j-stage

[5] 藤岡巧，岡島寛，松永信智：モデル誤差抑制補償器と周波数整形型終端状態制御の併用による3慣性ベンチマーク問題の一解法，計測自動制御学会論文集，Vol.50, No.12, pp.861-868 (2014) j-stage

[4] 岡島寛，西村悠樹，松永信智：モデル誤差抑制補償に基づく非線形システムのフィードバック線形化，計測自動制御学会論文集，Vol.50, No.12, pp.869-874 (2014) j-stage

[3] 梅井啓紀，岡島寛，松永信智，浅井徹：モデル誤差抑制補償器の多入出力システムに対する設計，システム制御情報学会論文誌，Vol.27, No.2, pp.67-72 (2014) j-stage

[2] 丸野裕太郎，A. T. Zengin，岡島寛，松永信智，中村憲仁：モデル誤差補償による福祉用前輪駆動型パーソナルビークルSTAVi の操縦特性の改善，JSME(C編), Vol.79, No.808, pp.4721-4733 (2013) j-stage

[1] H. Okajima, H. Umei, N. Matsunaga and T. Asai：A Design Method of Compensator to Minimize Model Error，SICE Journal of Control, Measurement, and System Integration, Vol.6, No.4, pp.267-275 (2013) (Open access)

[2] 岡島，松永：モデルと実対象の信号差を利用した制御，システム/制御/情報，Vol.60，No.2，pp.60-65 (2016)

[1] 岡島，松永：前輪駆動型電動車椅子に対する規範モデルに基づいた操縦性能改善，設計工学，Vol.50，No.4，pp.163-168 (2015)

International Conferences (with Links)

[13] R. Yoshida, Y. Tanigawa, H. Okajima and N. Matsunaga: A Design Method of Model Error Compensator using Meta-Heuristics and LMIs, Proceedings of the SICE Annual Conference 2020 pp. 1150-1155 (2020)

[12] Nobutomo Matsunaga, Naufal Bayu Fauzan, Hiroshi Okajima and Gou Koutaki, Archive Method of Stone Wall in Kumamoto Castle Lifted by Small CMG Crane using Model Error Compensator, 2019 12th Asian Control Conference , 18849231 (2019)

[11] Yuta Nakabayashi, Hiroshi Okajima, Nobutomo Matsunaga, Inter-Vehicle Distance Stabilization in Adaptive Cruise Control Using Signal Limitation Filter, Proceeding of 2018 IEEE International Conference on Systems, Man, and Cybernetics, pp.1985-1990 (2018)

[10] S. Sakamoto, T. Tanaka, H. Okajima and N. Matsunaga：Maneuverability evaluation of skid steer welfare vehicle for robust assistance control with model error compensator, Proceedings of ICCAS 2017 (2017)

[9] N. Matsunaga, H. Okajima and Y. Yamamoto：Robust variable stiffness control of McKibben type pneumatic artificial muscle arm by using multiple model error compensators, Proceedings of ICCAS 2017 (2017)

[8] Y. Nakabayashi, H. Okajima and N. Matsunaga：Signal limitation filter to satisfy velocity and acceleration constraints for arbitrary input signals, Proceedings of the SICE Annual Conference 2017

[7] T. Tanaka, H. Okajima and N. Matsunaga：Experiment of robust driving assistance control for skid steer welfare vehicle using model error compensator, Proceedings of ICCAS 2016 (2016) Outstanding Paper Award

[6] G. Ichimasa, K. Okumura, H. Okajima and N. Matsunaga：Extended structure of MEC for thermal process, Proceedings of the SICE Annual Conference 2016, pp.1593-1598 (2016)

[5] T.Sugano, H.Okajima and N.Matsunaga：Robust and precise platoon driving control of welfare vehicles along wheel track by using model error compensator, IECON2015, YF-001503

[4] T. Sugano, Y. Dan, H. Okajima, N. Matsunaga and Z. Hu：Indoor Platoon Driving of Electric Wheelchair with Model Error Compensator along Wheel Track of Preceding Vehicle, The 5th International Symposium on Advanced Control of Industrial Processes, 2014.5

[3] Y. Dan, H. Okajima, N. Matsunaga, Z. Hu and N. Nakamura：Experiment of Indoor Platoon Driving using Electric Wheelchair STAVi Controlled by Modeling Error Compensation System, ICT-PAMM Workshop on Mobility Assistance and Service Robotics, p26-31, 2013.11.

[2] Y. Maruno, Y. Dan, A. T. Zengin, H. Okajima and N. Matsunaga：Maneuverability Analysis of Front Drive Type Personal Vehicle STAVi using Modeling Error Compensation System, 7th IFAC Symposium on Advanced in Automative Control, 2013.9.

[1] H. Umei, H. Okajima, N. Matsunaga and T. Asai：A design method of compensator to minimize model error, SICE Annual Conference 2011, 2011.9.

Research on Model Error Compensator by Other Research Groups

Research on the Model Error Compensator by other research groups is extracted, particularly focusing on those that include "Model Error Compensator" in their titles.

T. Sano and S. Yamamoto, A Data-Driven Tuning Method for Model Error Compensator, Proc.of SICE 2018, 1199/2002 (2018)

H. Endo, R. Aramaki, K. Sekiguchi and K. Nonaka, Application of model error compensator based on FRIT to quadcopter, 2017 IEEE Conference on Control Technology and Applications (CCTA) (2017)

遠藤,関口,野中,モデル誤差補償器のオンライン調整法,計測自動制御学会論文集,55-3, 156/163(2019)

Y. Hatori, H. Nagakura, Y. Uchimura, Teleoperation with variable and large time delay based on MPC and model error compensator, IEEE International Symposium on Industrial Electronics(2021)

Y. Kawai, S. Nagao, Y. Yokokura, K. Ohishi,T. Miyazaki, Quick Torsion Torque ControlBased on Model Error Compensator and Disturbance Observer with Torsion Torque Sensor,IEEE/SICE International Symposium on SystemIntegration 2021 (2021)

S. Wakitani and T. Yamamoto, Design of a Database-Driven Model Error Compensator inSmart Model-Based Development, InternationalConference on Advanced Mechatronic Systems(2021)

鈴木元哉,制御入力速度飽和した初期実験データによるビークルのデータ駆動予測型制御器調整,電気学会論文誌C編,142-8, 959/970 (2022)

M. Suzuki and S Yahagi, Data-driven Design of Model Error Compensator and Fictitious Reference Signals for Vehicle Velocity Control of Autonomous Driving, 2022 22nd International Conference on Control, Automation and Systems (ICCAS) (2022)

川田昌克,モデル誤差抑制されたPID制御系のFRITを利用したパラメータ調整とLEGO教材による実験的検証,システム制御情報学会論文誌,Vol.37,No.1,31/33(2024)

川田昌克, 零点と不安定極をもたない2次系に対する外乱オブザーバとモデル誤差抑制補償器の関係について, 計測自動制御学会論文集, Vol. 60, No. 2, 101/103 (2024)

K. Shikada and N. Sebe, Relation between disturbance observer and model error compensator, 2023 SICE ISCS (2023)

脇谷伸, スマートMBDアプローチに基づく制御システム設計—モデルとデータを融合した新しいデジタルものづくりを目指して, システム/制御/情報, Vol. 67, No 8 pp. 343-348 (2023)

吉田, 石川, 南, データ駆動型フィードバック変調器による非線形補償器の設計, 計測自動制御学会論文集, Vol. 59, No. 5, pp. 252-258 (2023)

川田昌克, Arduino/LEGO教材を利用したPID制御の教育事例―経験則，モデルマッチングからデータ駆動制御，外乱補償まで― , 計測と制御, Vol. 63, No. 3, pp. 185-189 (2024)

松井, 川田, モデル誤差抑制補償器を併合する位置決め制御系の設計, システム制御情報学会誌, Vol. 37, No. 7, pp. 203-205, 2024

菅原，脇谷，山本，落合，富山，樹脂加工機械における階層型制御のためのGMV補償器の一設計，日本機械学会論文集

A. Haddi, M. E Azzouzi and M. Laabissi, A design approach of fractional model error compensator for fractional dynamical systems with polytopic uncertainty and disturbance | Circuits, Systems, and Signal Processing, Vol. 43, pages 7611-7633 (2024)

K. Osugi, R. Nishio, Y. Hanazawa, S. Sagara and R. Ambar, Force control experiment of a 3-link dual-arm underwater robot with model error compensator, The Thirtieth International Symposium on Artificial Life and Robotics 2025

R. Nishio, Y. Hanazawa, S. Sagara and R. Ambar, Experiments on resolved acceleration control of a 3-link dual-arm underwater robot with model error compensator, Artificial Life and Robotics 2025 https://doi.org/10.1007/s10015-025-01032-2

Domestic Conferences

(2024 onwards)

板宮敬悦，モデル誤差抑制補償要素を併用した適応制御系に関する研究，MSCS2024

板宮敬悦，ロバストモデル規範形適応制御系における固定補償要素のモデル誤差抑制制御器としての役割，SCI 2024

菅原貴弘，脇谷伸，山本透，落岩崇，富山秀樹，機械システムに対するGMV-MECの適用検討，MSCS2024

佐竹泰智, 楊熙, 萩原朋道, モデル誤差抑制補償器に基づくブーストコンバータの非線形出力電圧制御, 第69回システム制御情報学会研究発表講演会 (2025)

下東知隼, 澤田賢治, モデル誤差抑制補償器を用いた状態予測制御のロバスト化, 第69回システム制御情報学会研究発表講演会 (2025)

脇谷伸, 津田竜宏, MPCとMECによるパフォーマンス駆動型階層制御系の一設計, 第69回システム制御情報学会研究発表講演会 (2025)

This concludes the related articles on the Model Error Compensator. I have described the characteristics of the Model Error Compensator, comparisons with other methods, usage methods, and related research. This article concludes here.

I would be pleased if further research developments and practical applications are made based on these contents. The versatility of the Model Error Compensator (applicability to various types of systems) is high, so I believe there is great potential for further research developments.